SANAA, Yemen – Yemen's defiant Shiite rebels pressed their offensive in the country's south, apparently ignoring an overture from Saudi Arabia earlier this week, while the kingdom's warplanes continued to target their positions Thursday, officials said.

In a stunning development, Saudi Arabia had declared on Tuesday that it was halting coalition airstrikes targeting Yemen's Shiite rebels known as Houthis -- a four-week air campaign meant to halt the rebel power grab and help return to office embattled President Abed Rabbo Mansour Hadi, a close U.S. ally who fled Yemen.

The Decisive Storm operation was ending and a new phase called Restoring Hope was starting, focusing on diplomacy, humanitarian and counter-terrorism issues, the Saudis said at the time.

But hours after the announcement, new airstrikes hit the Iran-backed rebels and their allies on Wednesday -- suggesting the U.S.-backed offensive was being scaled back but not completely halted. Despite the renewed airstrikes, the initial Saudi announcement indicated a willingness to negotiate.

The bombardment also continued on Thursday, officials and witnesses said, as the Houthis sent reinforcements to the south, where their prized goal -- the port city of Aden -- remained an elusive goal, in part thanks to the Saudi-led airstrikes.

Meanwhile, Pakistan's top leaders, including Prime Minister Nawaz Sharif and army chief Gen. Raheel Sharif, arrived Thursday in Saudi Arabia to push for negotiations in the Yemen conflict. The two are to meet with King Salman to discuss the crisis, according to Pakisitan's Foreign Office spokeswoman Tasnim Aslam.

Both predominantly Sunni majority countries, Saudi Arabia and Pakistan are close allies, and Islamabad has supported the Saudi-led coalition though it declined to send troops, warplanes and warships to join it.

The kingdom and Gulf Arab allies launched the air strikes March 26, trying to crush the Houthis and allied military units loyal to ousted President Ali Abdullah Saleh.

The Saudis believe the rebels are tools for Iran to take control of Yemen. Iran has provided political and humanitarian support to the Houthis, though both Tehran and the rebels deny it has armed them.

Loud explosions shook the cities of Taiz and Ibb in western Yemen on Thursday, as well as Aden when coalition warplanes bombed the rebels and their allies, witnesses said.

Residents also said the Houthis and Saleh's forces were attacking the city of Dhale, one of the southern gateways to Aden, with random shelling.

All Yemeni officials and witnesses spoke on condition of anonymity because they were not authorized to talk to the media or feared for their safety amid the fighting.